An interesting hand.
Take board a match as an extreme form of matchpoints. Not only is there nothing that we can do against a making slam at the other table if the spades are 2-2, there also is nothing that we need to do against a failing slam at the other table if the spades are 3-1. In the first case you lose the board regardless of how you play the spades, in the second case you win the board no matter how you play the spades. So you may as well assume they are also in 4
at the other table, it's the only situation where your play makes a difference.
Now for imps. An imp is only an imp but for all that it's an imp.
First assume that they are in 4
at the other table.
Assume the other declarer plays the AK, but we play the A and then run the J.
If we are right, we make 680 to their 650. If we are wrong we make 650 to their 680. 1 imp our way if running the J is right, 1 imp their way if it is wrong.
Here the payoff/loss is equal.
Now assume that they are in 6S at the other table and, as is likely, declarer plays off the AK of trump.
Assume everyone is vul.
Assume that we run the J on the second round of trump. If we are wrong the score will be 1430 at the other table and 650 at ours. That's 780 and it only would have been 650 had we dropped the Q. 13 imps either way though, so it didn't cost. Now suppose we are right. We run the J and RHO shows out. We get 680 and at the other table it is -100 so that's 780. Had we gone up, it would be only 650 at our table, still -100 at the other, still no imp swing at all.
So it is one of those things where we can hope that they are in slam off 1 at the other table, but if that is so then it doesn't matter at all what we do at our table. So we go with whichever seems the most likely.
And what is the most likely lie? A few thoughts, largely inconclusive:
Of course playing for the drop has a slight a priori edge but often clues from the auction/play alter that. Is there anything? The silence of the opponents suggests that clubs are not 7-2, certainly not 8-1. That is not much. The lead of the A and small suggests he was hoping for a ruff. Maybe that helps? If he held Qxx would he want a ruff? Perhaps. He might imagine taking the A, leading to his partner's hypothetical K, getting a ruff and then some miracle occurring that gives their side another trick. But then he might equally figure that if his partner has the K they are getting two diamonds anyway, that he might well be getting his trump Q in normal play, and that the chance of a fourth trick is better if he doesn't rush in.
So we might reason that he is more likely to have gone after the ruff holding trump xx than with trump Qxx. But this has to be balanced against the fact that if he has only two diamonds he is less likely to have a second doubleton.
All in all, I went with the AK but on another day it would have been wrong.